We had a power outage and I used a power source (battery to AC) to power up our handy phones and it worked.
But you can't be sure that a power cut won't bring down the cell tower or other gear outside your home.
As such, when there's a city wide power outage, nothing can be assured about what will stay up. Here the cell towers have backup power for reasons. You may want to ask the carriers why they didn't stay up.
I'm considering cutting the landline cord. The ONLY reason I keep it is for emergencies. But cable phone service is $20 vs the $70 I pay for landline, so you see the concern.
Unfortunately, the cable phone only comes with an 8 hour battery backup. The battery backup is a proprietary (from what they tell me) battery that plugs into the phone modem with they install. Now, I have internet service through my cable provider as well. My phone supports calling over wifi. So, if I attached a UPS to my cable modem and router (the cable modem is a separate device from the phone modem), would I be able to call out on my cell phone in case of a power outage?
Also be advised that I found out during our last power outage that the cell towers also go down, so calling directly from my cellphone using my data plan was useless. My apologies for being a bit obsessive. But there's a huge gap between $20 a month and $70 a month.